Center of Gravity: Where Does it Lead?

[disregardthat]

I was wondering, center of gravity is the point in the object where other objects are pulled to. (they want to get to the center, but the onject itself is stopping it, like we won't fall to the center of the earth, because the eart itself are stopping us.)

Anyway, let's assume that. What if we dug a hole from the top of the earth, (assuming the Earth is a perfectly shaped round ball) straight to the other side, and in the middle, digging out a room with let's say 20 km in diameter. If we jumped into this hole, (with air resistance) would we then in the end be at the gravity center of the earth? (since if you cut the Earth in 2, the mass of these would be the same, the digging removed the same mass on each sides.) Would we float in the middle?

 

[Danger]

There's quite an extensive discussion of this from a while back, if you want to do a search.
Basically, you would fall right through to the other side, then back to almost where you started from, then repeat. Because of the air resistance, each trip would be a little shorter than the one before, so you would end up settling in the middle.

 

[D H]

I was wondering, center of gravity is the point in the object where other objects are pulled to. (they want to get to the center, but the onject itself is stopping it, like we won't fall to the center of the earth, because the eart itself are stopping us.)

That is not the standard definition of "center of gravity". The center of gravity of an object is the point (generally inside the object) such that the gravitational acceleration at that point is the same as the gravitational acceleration experienced by the object. Center of gravity is a near-synonym to center of mass, and is treated as an exact synonym in most applications.

 

[DaveC426913]

As Danger points out, if you fell to the centre of the Earth, you'd oscillate.

But if you climbed down, or fell and managed to stop your fall near the end, well then, yes you would find yourself floating somewhere in your 20 km cavern. You would experience weightlessness everywhere in that cavern (even near the walls - it can be shown that the net gravitational pull anywhere inside a hollow sphere - even one 4000 miles thick - is zero).

 

[ranger]

it can be shown that the net gravitational pull anywhere inside a hollow sphere - even one 4000 miles thick - is zero)

Can you please elaborate on this.

 

[Danger]

I can't give you any equations, which the others can, because I have no math education. I can understand it intuitively, though, so that's how I'll express it.
Suppose that you're in the centre. You no doubt realize that there is equal mass pulling at you from all directions, so the gravity balances out. Now, let's say you move straight up 1/2 radius of the cavity. You are now much closer to part of the mass, so it pulls at you more strongly than it did before. On the other hand, though, there is much more mass pulling the other way, which balances it out again. The closer you get to one side, the more mass there is on the other. It always evens out.
Nice new avatar, by the way.

 

[neutrino]

Can you please elaborate on this.

Look up/google "Gauss' Law." Usually, you'll end up with stuff on electrostatics, but it's a simple task to derive the result for gravitostaics, the principle is the same.

 

[DaveC426913]

Can you please elaborate on this.

I went looking for a nice, concise explanation, but I decided it would be easier if you found the type of answer (math vs. intuitive) that suited you.

Simply Google "gravity inside hollow sphere". There have been numerous discussions on this board about it as well, though I'm not impressed with PF's search feature.

http://en.wikipedia.org/wiki/Divergence_theorem" has this to say:

... a hollow sphere does not produce any gravity inside. The gravitational field inside is the same as if the hollow sphere were not there (i.e. the field is that of any masses inside and outside the sphere only).

 

[arildno]

Remember that the main reason why we might be interested in finding a single point so that the entire force may be said to act there, instead of regarding its effect as distributed, is when we are interested in calculating the TORQUE of the force about some other point.

Thus, "the centre of gravity", if it exists, is such a point that the net torque due to gravity wrt. to some other point can be represented as the cross product between the net gravitational force vector and the distance vector between the reference point and the centre of gravity.
I have made a note of this here:
https://www.physicsforums.com/showthread.php?t=95524[/URL]

 

[Doc Al]

...though I'm not impressed with PF's search feature.

Me neither. I have found that the best way to search for items on PF is to use Google, restricting the search domain to this site. Works great!

This topic comes up regularly. Here's a thread I found in seconds (using Google): https://www.physicsforums.com/showthread.php?t=121120"

 

[ranger]

Thanks for the input guys. It makes more sense now :)

 

[DaveC426913]

use Google, restricting the search domain to this site.

Brilliant. Thanks I'll do that from now on.


Also. I didn't know you could do that for any site. Now I do.

 

[Danger]

Hell of a great idea there, Doc. I had no idea that you could restrict a Google search to one site. Even without doing that, I once used it to find a long-lost thread hereabouts.

 

[disregardthat]

Would gravity cancel out if the objects are too far from each other. let's say there were 2 objects in the world, 1 kg. and they were several millions of years away from each other. they stood perfectly still in compare to oneanother, would they slide towards each other?

 

[DaveC426913]

Would gravity cancel out if the objects are too far from each other. let's say there were 2 objects in the world, 1 kg. and they were several millions of years away from each other. they stood perfectly still in compare to oneanother, would they slide towards each other?

Gravity works over unlimited distances. Yes, they would eventually move toward each other, with two caveats:
- we must discount other phenomoena such as the expansion of the universe. This may or may not offset the closing distance.
- we must allow enough time. (Those two objects might take longer than the age of the universe to reach each other.)

Note that our galaxy is being pulled towards a point in space many millions of light years away by the large collection of our local clusrter of galaxies. Those galaxies, while there is a lot of mass in them, are still, ultimately made of itty-itty atoms, each of which exerts its own pull on us.

 

[disregardthat]

Oh, I have another question. I read that the big bang didnt accelerate the mass, it just expanded the space between the mass. Why is that the galaxies is not moving towards each other now?

 

[Danger]

The universe is still expanding. If/when that stops, gravity will bring things back together.

 

[ranger]

The universe is still expanding. If/when that stops, gravity will bring things back together.

So the enormous energy of the big bang is still causing the universe to expand? And when you said everything would come back together, does this mean that there will certainly be a "big crunch"?

 

[Danger]

If things begin contracting gravitationally, then there must be a 'big crunch' as I understand the term, since there is certainly more than enough mass that it will form a black hole. I do not know whether or not space-time itself will also be contracted to a singularity. Check with the Tiger about that.

 

[DaveC426913]

Oh, I have another question. I read that the big bang didnt accelerate the mass, it just expanded the space between the mass. Why is that the galaxies is not moving towards each other now?

It is more accurate to say that, on average, galaxies are moving away from each other.

Some galaxies are moving towards each other. For example our nearest neighbour, Andromeda is racing towards us.

 

[ranger]

For example our nearest neighbour, Andromeda is racing towards us.

I'll take that statement literally. Is it drawn to us because of our galaxy's gravitational pull? Can it also be said that we are racing towards Andromeda? because for some reason I have picture of our milky way moving [not in the direction of Andromeda] and Andromeda just sipralling towards us.

 

[disregardthat]

Well, it is clearly a big difference in the velocity of the galaxies, and the space between them expanding so the distance to oneanother is increasing.
When you say the universe is expanding, there ARE something "outside" it right? Like infinite space? It would only make sense.

When the universe is expanding, is it the "lenght" between each Planckmeter that is increasing? or just adding more space (plankcmeters)

 

[DaveC426913]

I'll take that statement literally. Is it drawn to us because of our galaxy's gravitational pull? Can it also be said that we are racing towards Andromeda? because for some reason I have picture of our milky way moving [not in the direction of Andromeda] and Andromeda just sipralling towards us.

Andromeda is as big as The Milky Way; we are drawn towards each other. We are part of a large collection of galaxies called the local cluster that are gravitationally bound. We are also as a group in the grips of an even larger "supercluster". There is a whole structure to matter density on the supergalactic scale.